Comparing Two Novel LiDAR-Based Indices for Quantifying Forest Structural Complexity

Forest structural complexity is critical for ecosystem functions, yet standardized metrics for its quantification remain elusive. This study compares two LiDAR-derived three-dimensional indices, the box dimension ( $D_b$ ) as a fractal-based measure, and canopy entropy ( $\mathrm{CE}$ ), an entropy-based metric, to evaluate their methodological, computational, and conceptual differences. Using mobile LiDAR scans from $15m\times 15m$ forest plots in Maine, USA, and Nova Scotia and New Brunswick, Canada, we analyzed 170 point clouds to assess correlation, computation time, and theoretical underpinnings. Statistical analysis revealed a strong linear relationship between $D_b$ and $\mathrm{CE}$ (Pearson's $r=0.823,p<0.001$ ), with Deming regression indicating $\widehat{\mathrm{CE}}=4.75\times D_b-1.07$ . Also, $\mathrm{CE}$ computation averaged 40 times slower than $D_b$ , scaling roughly linearly with point cloud size. Conceptually, $D_b$ reflects fractal dimensionality linked to physiological process optimization, while $\mathrm{CE}$ quantifies biomass distribution homogeneity. ${\mathrm{CE}}^{\text{'}}$ s unit dependence on plot size limits cross-study comparability, whereas ${D_b}^{\text{'}}$ s dimensionless fractal interpretation offers broader intuitiveness. Both indices address sampling density bias but differ in parameterization and data efficiency. Despite ${\mathrm{CE}}^{\text{'}}$ s theoretical novelty, it does not surpass $D_b$ in interpretability, precision, or speed, and its proposed advantage in capturing higher complexity remains unsubstantiated. Despite their conceptual distinctions, their strong correlation suggests competitive rather than complementary roles. Future research should explore biome-specific variability and physiological links to ecosystem functions to refine their utility in forest management under climate change.